Method of Protein Fitting Into the Symmetric Cryo-EM Density Maps Based on Gaussian Curvature

To solve the problem of low resolution of three-dimensional symmetric biomacromolecule structure obtained by cryo-electron microscopy (cryo-EM) density maps, a new method based on Gaussian curvature calculation was proposed. The new feature points were defined by calculating the discrete Gaussian curvature of the protein and the symmetrical cryo-EM density maps. For the symmetrical cryo-EM density maps, the K-means method was used to define the corresponding feature points. The corresponding feature points were matched by the cross correlation score of root mean square deviation (RMSD) values and Gaussian curvature and the optimization model. The rotation matrix and the translation vector were then calculated using the least squares method. Finally, the other parts were fitted into the symmetrical cryo-EM density map in the same way. The Gaussian curvature of ellipsoid was calculated, x^2 + \fracy^22 + \fracz^23 = 1, and the analyzed Gaussian curvature was compared with the numerical Gaussian curvature. The Gaussian curvature of the protein 1DOR was calculated and the feature point was also calculated. The fitting results of the macromolecules assembly of protein 1DOR and 2REC were visualized. The numerical experiments show that this method is accurate and effective.